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Simplifying Fractions/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. Tim is reading a book. He has tears in his eyes and is quietly sniffling. Moby zaps the book with a ray gun. It shrinks to a tiny size. TIM: Hey, I was reading tha— Moby zaps Tim's box of tissues. It shrinks, too. TIM: A shrink-ray, huh? Maybe that’ll come in handy for this: Tim holds up a typed letter and reads from it. TIM: Dear Tim and Moby, how do you reduce fractions? From, Zeb. Let’s see if Moby can answer that. MOBY: Beep! Tim places a fraction, sixteen twenty-fourths, on the table. Moby zaps the fraction with the shrink-ray. Instead of shrinking in size, the fraction turns into another fraction, two-thirds. Moby checks to see if his shrink-ray is working properly. MOBY: Beep! TIM: What do you mean, it didn't work? You just reduced a fraction! Reducing a fraction means simplifying it so that the numerator and denominator are both as small as they can possibly be. MOBY: Beep? TIM: No, no, the value of the fraction stays the same when you reduce it. That's why most mathematicians prefer to use the word "simplify." The point is to make it as simple as possible! Remember when we ordered that pizza last week? We got the usual: half pepperoni, and half ball-bearings and screws. An animation shows a man delivering a pizza to Tim's house. Half of the pizza is topped with pepperoni and the other half has ball-bearings and screws. TIM: The pizza had six slices. The pizza divides into six equal slices: three pepperoni, and three ball-bearings and screws. TIM: But when we called to order, we didn’t ask for three-sixths pepperoni, and three-sixths metal. We asked for half and half. An animation shows another pizza of equal size. It has been divided in half. Three-sixths of the first pizza is the same size as one half-slice of pizza. TIM: That’s because three-sixths is the same as one-half! In mathematical terms, they’re equivalent fractions. An equation reads, three-sixths equals one-half. MOBY: Beep! TIM: What do you mean, I should stop using pizza to illustrate math concepts? I like pizza. Anyway, to simplify a fraction, you first have to find the greatest common factor of the numerator and the denominator. That’s the largest number that will divide evenly into both. Let’s say you’re given the following fraction: twelve-twentieths. Tim places the fraction, twelve-twentieths, on the table. TIM: To find the greatest common factor, you can make a list of all the factors of 12 and 20, and then pick the biggest one they have in common. Tim eyes Moby's shrink-ray. TIM: Hey, can you set that thing on "factor?" Moby adjusts the shrink-ray and zaps the numerator, 12. Its factors appear. TIM: So the factors of 12 are one, two, three, four, six, and 12. Moby zaps the denominator, 20. Its factors appear. TIM: And the factors of 20 are one, two, four, five, 10, and 20. Looks like the greatest common factor is four! MOBY: Beep? TIM: To simplify that fraction, you just divide both the numerator and denominator by their greatest common factor. 12 divided by four is three, so our numerator is three. An equation appears, reading, 12 divided by four equals three. TIM: And 20 divided by four is five, so our denominator is five. An equation appears, reading, 20 divided by four equals five. TIM: So twelve-twentieths, written in the simplest possible terms, is three-fifths! An equation appears, reading, twelve-twentieths equals three-fifths. TIM: Let’s try it again, with four-fourteenths. The new fraction appears. TIM: Let’s see. The factors of four are one, two, and four, and the factors of 14 are one, two, seven, and 14. The factors of the numerator and denominator appear. TIM: Looks like the greatest common factor is two. So the next step is— MOBY: Beep! TIM: Right—dividing the numerator and the denominator by two! Four divided by two is two, and 14 divided by two is seven. The animation shows the calculations that Tim describes. TIM: So four-fourteenths simplifies to two-sevenths! An equation appears, reading, four-fourteenths equals two-sevenths. MOBY: Beep? TIM: Well, if there are no common factors, the fraction can’t be rewritten—it’s already in its simplest form. Now, can I have my book back? An animation shows Tim holding up the tiny book. MOBY: Beep! TIM: What do you mean, there’s no enlarging ray?! How am I supposed to find out if Adrienne and Paul live happily ever after? MOBY: Beep! Moby zaps Tim with the shrink-ray. Tim is now small enough to read his book. He speaks in a high-pitched voice. TIM: Gee, thanks a lot! Crazy robot. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts